Question

(a) Ram is training for his school's annual sports meet. He earlier used to run at 8 m/s, now after training, he has increased his speed by $\frac{1}{2}$ times his original speed. Find how much time will Ram take to complete a 100m race.

(b) List four rational numbers that lie between $\frac{5}{7}$ and $\frac{7}{8}$
[4 MARKS]

Answer 1

Each part: 2 Marks

(a) Original speed of Ram $=8$m/s

After training, his speed has increased to = $8+\frac{1}{2}\times 8=12$m/s

Time taken to complete the 100m race $=\frac{100}{12}=\frac{25}{3}$ seconds.


(b) One of the methods is taking the average of the two rational numbers. Let's do it with LCM method here.

Taking LCM of 7 and 8 = 56

$\Rightarrow \frac{5}{7}=\frac{5\times 8}{7\times 8}=\frac{40}{56}$

$\Rightarrow \frac{7}{8}=\frac{7\times 7}{8\times 7}=\frac{49}{56}$

$\therefore$ Four rational numbers between $\frac{40}{56}$ and $\frac{49}{56}$ can be $\frac{43}{56},\frac{44}{56},\frac{45}{56},\frac{46}{56}$

In standard form the rational numbers are $\frac{43}{56},\frac{11}{14},\frac{45}{56},\frac{23}{28}$